Knowledge of the gravity-free shape of a flexible object such as a glass sheet is of value in terms of understanding and controlling 1) the process used to make the object, e.g., a downdraw fusion process in the case of glass sheets, and 2) the behavior of the object during use, e.g., the behavior of a glass sheet when vacuum chucked to a flat plane. See, for example, commonly-assigned U.S. Pat. No. 7,509,218 and PCT Patent Publication No. WO 2009/108302, the contents of both of which are incorporated herein by reference in their entireties.
Determining the gravity-free shape of glass sheets used as substrates in display devices has become particularly challenging as the sheets have become larger and thinner. For example, GEN 10 substrates for liquid crystal displays have an area of greater than nine square meters (2,880×3,130 mm) and a thickness of 0.7 mm, with even thinner sheets becoming ever more popular. Although the “bed-of-nails” (BON) techniques of U.S. Pat. No. 7,509,218 can be used with such larger and thinner sheets, the number of measuring assemblies (i.e., the number of adjustable pin and load cell combinations) needed to achieve high resolution becomes substantial as the glass sheet becomes larger. This, in turn, leads to high equipment costs. Also, errors due to a defective measuring assembly become more common as the number of assemblies increases. Further, the preferred algorithm of U.S. Pat. No. 7,509,218 for adjusting the heights of the adjustable pins fixes the locations of three of the pins. In practice, such fixed heights cause shape errors to concentrate at the locations of the sheet supported by the fixed-height pins, which may compromise the accuracy of the shape determination.
The present disclosure provides 1) methods and apparatus for achieving higher resolution for a given number of measuring assemblies, 2) methods and apparatus for confirming the reliability of shape determinations, and 3) methods and apparatus for distributing shape errors over an entire set of adjustable-pin/load-cell assemblies. These features can be used singly or in combinations, and thus can be used to address some or all of the above problems relating to the determination of gravity-free shapes using BON techniques.